1 // Copyright (c) 2015 John Maddock
2 // Use, modification and distribution are subject to the
3 // Boost Software License, Version 1.0. (See accompanying file
4 // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
5
6 #ifndef BOOST_MATH_ELLINT_HL_HPP
7 #define BOOST_MATH_ELLINT_HL_HPP
8
9 #ifdef _MSC_VER
10 #pragma once
11 #endif
12
13 #include <boost/math/special_functions/math_fwd.hpp>
14 #include <boost/math/special_functions/ellint_rj.hpp>
15 #include <boost/math/special_functions/ellint_rj.hpp>
16 #include <boost/math/special_functions/ellint_1.hpp>
17 #include <boost/math/special_functions/jacobi_zeta.hpp>
18 #include <boost/math/constants/constants.hpp>
19 #include <boost/math/policies/error_handling.hpp>
20 #include <boost/math/tools/workaround.hpp>
21
22 // Elliptic integral the Jacobi Zeta function.
23
24 namespace boost { namespace math {
25
26 namespace detail{
27
28 // Elliptic integral - Jacobi Zeta
29 template <typename T, typename Policy>
heuman_lambda_imp(T phi,T k,const Policy & pol)30 T heuman_lambda_imp(T phi, T k, const Policy& pol)
31 {
32 BOOST_MATH_STD_USING
33 using namespace boost::math::tools;
34 using namespace boost::math::constants;
35
36 const char* function = "boost::math::heuman_lambda<%1%>(%1%, %1%)";
37
38 if(fabs(k) > 1)
39 return policies::raise_domain_error<T>(function, "We require |k| <= 1 but got k = %1%", k, pol);
40
41 T result;
42 T sinp = sin(phi);
43 T cosp = cos(phi);
44 T s2 = sinp * sinp;
45 T k2 = k * k;
46 T kp = 1 - k2;
47 T delta = sqrt(1 - (kp * s2));
48 if(fabs(phi) <= constants::half_pi<T>())
49 {
50 result = kp * sinp * cosp / (delta * constants::half_pi<T>());
51 result *= ellint_rf_imp(T(0), kp, T(1), pol) + k2 * ellint_rj(T(0), kp, T(1), T(1 - k2 / (delta * delta)), pol) / (3 * delta * delta);
52 }
53 else
54 {
55 T rkp = sqrt(kp);
56 T ratio;
57 if(rkp == 1)
58 {
59 return policies::raise_domain_error<T>(function, "When 1-k^2 == 1 then phi must be < Pi/2, but got phi = %1%", phi, pol);
60 }
61 else
62 ratio = ellint_f_imp(phi, rkp, pol) / ellint_k_imp(rkp, pol);
63 result = ratio + ellint_k_imp(k, pol) * jacobi_zeta_imp(phi, rkp, pol) / constants::half_pi<T>();
64 }
65 return result;
66 }
67
68 } // detail
69
70 template <class T1, class T2, class Policy>
heuman_lambda(T1 k,T2 phi,const Policy & pol)71 inline typename tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi, const Policy& pol)
72 {
73 typedef typename tools::promote_args<T1, T2>::type result_type;
74 typedef typename policies::evaluation<result_type, Policy>::type value_type;
75 return policies::checked_narrowing_cast<result_type, Policy>(detail::heuman_lambda_imp(static_cast<value_type>(phi), static_cast<value_type>(k), pol), "boost::math::heuman_lambda<%1%>(%1%,%1%)");
76 }
77
78 template <class T1, class T2>
heuman_lambda(T1 k,T2 phi)79 inline typename tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi)
80 {
81 return boost::math::heuman_lambda(k, phi, policies::policy<>());
82 }
83
84 }} // namespaces
85
86 #endif // BOOST_MATH_ELLINT_D_HPP
87
88